Can the angle of refraction be equal to the angle of incidence?

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SUMMARY

The discussion centers on Snell's law, which states that n1sin(theta1) = n2sin(theta2). It clarifies that the angle of refraction (theta2) can equal the angle of incidence (theta1) when both angles are 90 degrees or when light travels through two transparent substances with identical refractive indices. The example of a Pyrex rod in Wesson oil illustrates that even with the same refractive index, one can conceptually consider an interface, leading to theta1 equaling theta2. This confirms that light can pass straight through without deviation when no actual interface exists.

PREREQUISITES
  • Understanding of Snell's Law and its mathematical formulation
  • Knowledge of refractive indices and their significance in optics
  • Familiarity with the concept of light propagation through different media
  • Basic principles of geometric optics
NEXT STEPS
  • Study the applications of Snell's Law in optical devices
  • Explore the behavior of light at interfaces with varying refractive indices
  • Investigate the properties of materials like Pyrex and their refractive indices
  • Learn about total internal reflection and its implications in fiber optics
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Students of physics, optical engineers, and anyone interested in the principles of light behavior at interfaces will benefit from this discussion.

bobaustin
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Snell's law says
n1sin(theta1) = n2sin(theta2)

The angle of refraction theta2 can be greater or less than the angle of incidence theta1. That's fairly obvious.

My question is if theta2 = theta1 then we don't have an interface (because n1 = n2) so the light is still in the same medium, and there is nothing to talk about?

Is there a case where there is an interface and theta2 = theta1 ?

--------------------------------

I think I found the answer: Pyrex rod in Wesson oil!
 
Last edited:
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You can always pretend that there's an interface, with each side having the same n. Snell's law then tells you that θ1 = θ2, which makes sense since it just means that the light continues straight through as if there was no interface (which there isn't, of course).
 
Doc Al said:
You can always pretend that there's an interface, with each side having the same n. Snell's law then tells you that θ1 = θ2, which makes sense since it just means that the light continues straight through as if there was no interface (which there isn't, of course).

How about the case that the OP pointed out: two transparent substances with the same index of refraction?

Of course, angle of incidence is also equal to the angle of refraction with the former is 90 degrees.
 

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